The twisted bird skull necklace is a Dungeoneering reward. It is the cheapest bone necklace available. This item requires 30 Prayer and 30 Dungeoneering to obtain and equip. This necklace restores Prayer points when burying certain bones - the number of prayer points was secretly reduced on 30 April2013:

Note that manually scattering ashes will not restore prayer points when using the necklace, nor will ghosts killed in conjunction with the ectoplasmator. Only ghosts killed or ashes scattered automatically by the attuned ectoplasmator will trigger the effects of the necklace.

It is the only way for non-member players to gain Prayer points other than praying at an altar, levelling up, or dying.
The necklace may be of use in the Wilderness, as there is a large supply of bones usually available that can be used to restore Prayer points, if an altar is not within reach. If player killing, it is unwise to bring this with you because the space required to hold bones is better served holding high-healing food or potions.

The necklace can be used together with the bonecrusher to gain 50 Prayer points every time you kill a monster that drops bones as remains, or with the attuned ectoplasmator when killing ghosts or demons. This can be useful to sustain prayers for longer periods of time in combat.

In theory, this necklace is an inexpensive alternative to training on weak monsters, if the player has high enough Constitution and the Redemption prayer. By burying bones it is possible to gain just 100 Prayer points to trigger redemption when life points are low. However this method can be used only by members and doesn't work with players with a low Constitution level.

Some high levelled people often use this amulet in free-to-play as a replacement for the prayer potions in members. As bones are less in value then swordfish, this amulet is great for training, without wasting a lot of money or food.